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在用岭回归弥补线性回归的不足主题中，我们介绍了岭回归优化的限制条件。我们还介绍了相关系数的先验概率分布的贝叶斯解释，将很大程度地影响着先验概率分布，先验概率分布通常均值是0。
因此，现在我们就来演示如何scikit-learn来应用这种解释。









Getting ready¶








岭回归和套索回归（lasso regression）用贝叶斯">
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<article class="post-text h-entry hentry postpage" itemscope="itemscope" itemtype="http://schema.org/Article"><header><h1 class="p-name entry-title" itemprop="headline name"><a href="#" class="u-url">directly-applying-bayesian-ridge-regression</a></h1>

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                    Tao Junjie
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            <p class="dateline"><a href="#" rel="bookmark"><time class="published dt-published" datetime="2015-08-18T12:57:47+08:00" itemprop="datePublished" title="2015-08-18 12:57">2015-08-18 12:57</time></a></p>
            
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<h2 id="贝叶斯岭回归">贝叶斯岭回归<a class="anchor-link" href="directly-applying-bayesian-ridge-regression.html#%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%B2%AD%E5%9B%9E%E5%BD%92">¶</a>
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<p>在<em>用岭回归弥补线性回归的不足</em>主题中，我们介绍了岭回归优化的限制条件。我们还介绍了相关系数的先验概率分布的贝叶斯解释，将很大程度地影响着先验概率分布，先验概率分布通常均值是0。</p>
<p>因此，现在我们就来演示如何scikit-learn来应用这种解释。</p>
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<h3 id="Getting-ready">Getting ready<a class="anchor-link" href="directly-applying-bayesian-ridge-regression.html#Getting-ready">¶</a>
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<p>岭回归和套索回归（lasso regression）用贝叶斯观点来解释，与频率优化观点解释相反。scikit-learn只实现了贝叶斯岭回归，但是在<em>How it works...</em>一节，我们将对比两种回归算法。</p>
<p>首先，我们创建一个回归数据集：</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <span class="n">make_regression</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_regression</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">n_informative</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
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<h3 id="How-to-do-it...">How to do it...<a class="anchor-link" href="directly-applying-bayesian-ridge-regression.html#How-to-do-it...">¶</a>
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<p>我们可以把岭回归加载进来拟合模型：</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">BayesianRidge</span>
<span class="n">br</span> <span class="o">=</span> <span class="n">BayesianRidge</span><span class="p">()</span>
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<p>有两组相关系数，分别是<code>alpha_1 / alpha_2</code>和<code>lambda_1 / lambda_2</code>。其中，<code>alpha_*</code>是先验概率分布的$\alpha$超参数，<code>lambda_*</code>是先验概率分布的$\lambda$超参数。</p>

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<p>首先，让我们不调整参数直接拟合模型：</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">br</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">br</span><span class="o">.</span><span class="n">coef_</span>
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<pre>array([ -1.39241213,   0.14671513,  -0.08150797,  37.50250891,
         0.21850082,  -0.78482779,  -0.26717555,  -0.71319956,
         0.7926308 ,   5.74658302])</pre>
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<p>现在，我们来调整超参数，注意观察相关系数的变化：</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">br_alphas</span> <span class="o">=</span> <span class="n">BayesianRidge</span><span class="p">(</span><span class="n">alpha_1</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">lambda_1</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">br_alphas</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">br_alphas</span><span class="o">.</span><span class="n">coef_</span>
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<pre>array([ -1.38807423,   0.14050794,  -0.08309391,  37.3032803 ,
         0.2254332 ,  -0.77031801,  -0.27005478,  -0.71632657,
         0.78501276,   5.71928608])</pre>
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<h3 id="How-it-works...">How it works...<a class="anchor-link" href="directly-applying-bayesian-ridge-regression.html#How-it-works...">¶</a>
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<p>因为是贝叶斯岭回归，我们假设先验概率分布带有误差和$\alpha$参数，先验概率分布都服从$\Gamma$分布。</p>
<p>$\Gamma$分布是一种极具灵活性的分布。不同的形状参数和尺度参数的$\Gamma$分布形状有差异。<strong>1e-06</strong>是 scikit-learn里面<code>BayesianRidge</code>形状参数的默认参数值。</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline

<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="k">import</span> <span class="n">gamma</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

<span class="n">form</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="s2">"loc=</span><span class="si">{}</span><span class="s2">, scale=</span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">g</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1e-06</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mf">1e-06</span><span class="p">:</span> <span class="n">gamma</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
<span class="n">g2</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1e-06</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">1</span><span class="p">:</span> <span class="n">gamma</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
<span class="n">g3</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1e-06</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">2</span><span class="p">:</span> <span class="n">gamma</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">rng</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="n">form</span><span class="p">(</span><span class="mf">1e-06</span><span class="p">,</span> <span class="mf">1e-06</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'r'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">g2</span><span class="p">,</span> <span class="n">rng</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="n">form</span><span class="p">(</span><span class="mf">1e-06</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'g'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">g3</span><span class="p">,</span> <span class="n">rng</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="n">form</span><span class="p">(</span><span class="mf">1e-06</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Different Shapes of the Gamma Distribution"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span>
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2bBizZs1KSH4jRozg9NNPZ/fu3Tz00ENceeWV7Ny5s3r997//fXJzc9m0aRM7%0AduzgJz/5SUL2W0NjT+Cf4JsBmDS8bfu3GZOx5duWN3ZR5BiX7P/zhYWFtmDBAjMzKysrs/Hjx1tu%0Abq7l5ubaHXfcYYcOHapO+9e//tX69etnWVlZdsIJJ9icOXPqtM8//vGPNnjw4COW//3vf7dvfetb%0A1r59e+vXr58tXLgwbB533XWXjRw5svr12rVrLS0tzQ4cOGBmZiNGjLB77723TuUrKiqy008/3bKy%0AsqxLly42ceLE6nWLFi2qLmNeXp796U9/MjOzt956y/r3729ZWVmWl5dnkydPrt7miy++MOecVVRU%0AmJnZ3r177Yc//KHl5ORYt27d7Oc//3n1ungFAgFzztmGDRtqLI9nH6tWrbJWrVpVnzszs/POO8/+%0A8Ic/mJnZ3LlzrbCwMKYyhvu8+8sjxkfV7CVupeWq2YvE66GHHqK4uJjly5ezfPlyiouLefDBBwEo%0ALi7m+uuv5/HHH6ekpIQPP/yQwsJCAG677Tays7NDPvr37x/Tvrds2cLw4cO599572bNnD4899hhX%0AXHFFjdplsJUrV9KvX7/q18cffzytWrVi9erVABQVFWFm9O3bl9zcXEaNGnVEM38448ePZ8KECZSU%0AlLBu3TquuuoqADZs2MCwYcMYP348O3fuZNmyZdXHl5GRwbRp0ygpKeHtt9/mqaeeYvbs2SHzv+GG%0AG0hLS2Pt2rV8/PHHzJs3j2effRaAxYsXhz2X2dnZfPTRRzEdQ6R91LZixQqOP/540tPTq5f169eP%0AFStWALB06VJOOukkrr/+eo477jjOPPNMPvzww5jKEZdovwaa0oMk/5XfXKz8cqUxGVuwbkFjF0WO%0AcTH9z0P9H3UUXLM/4YQT7N13361eV1WjMzO76aabatRw6yNUzf7RRx+1UaNG1Vh28cUX29SpU0Pm%0AceGFF9rTTz9dY1m3bt3sgw8+MDOzli1bWo8ePezzzz+3AwcO2BVXXFGjJSCS8847zyZNmmQ7duyo%0Asfzhhx+273//+zHlMX78eJswYYKZ1azZb9u2zVq1amWlpaXVaadPn25DhgyJKd/aQtXs493Hiy++%0AaGeddVaNZXfffbfdcMMNZmZ24403mnPOnn/+eSsvL7dXXnnF2rdvbzt37jwir3Cfd1Szl4ZQVl4G%0AqGYvTUQiwn0CbN26lYKCgurX+fn5bN26FYDNmzdzwgknJGQ/oWzYsIGZM2fWqMUuWbKEbdu2sXjx%0AYjIzM8nMzOTUU08FvJp0SUlJjTxKSkrIzMwEoG3btowZM4aePXuSnp7O3XffzTvvvBNTWZ577jlW%0Ar15N7969OfPMM3n77bcB7xwcf/zxIbcpKipiyJAhdO7cmfbt2/P000+za9eukMcZCATIycmpPs5b%0AbrmFHTt2xHyuoom2j5NPPpnMzEyysrJYsmQJmZmZ7Nu3r0YeJSUlZGVlAdCmTRt69OjBmDFjSE1N%0A5eqrryYvL48lS5YkrMyg6XKlDqqa8Q8ePtjIJRFpOnJzc1m/fj29e/cGYOPGjXTr1g2AvLw81qxZ%0AE3K7qgvlQiksLOSTTz6psSzU1f/5+fmMGjWKZ555JmQ++/fXHEZ78skns3z58urXa9eu5fDhw5x4%0A4okA9O3bN2Q+sejZsyfTp08HYNasWVx55ZXs2rWLvLw8iouLQ25z7bXXMm7cOObOnUtaWhoTJkwI%0A2QWRl5dHq1at2LVrFykpR9ZlFy1axLBhw8KWbc6cOZx99tkRyx9tH1XN81VWr17NunXrOHDgABkZ%0AGQAsX76cUaNGAV6T/ltvvVVjmwYZxRGt6t+UHqgZ/6h4b+17xmTs+f/3fGMXRY5xyf4/H9yM//Of%0A/9wGDRpkO3bssB07dtjZZ59t99xzj5mZFRcXW/v27W3BggVWUVFhmzdvts8++yyufVVUVFhpaak9%0A9dRTdt5551lZWZkdPnzYzMw2bdpkXbt2tblz51p5ebmVlpba+++/b5s3bw6Z14oVKywrK8sWLVpk%0ABw4csBEjRtiIESOq1z///PPWo0cPW7dunR08eNB+8IMf2OjRo6vXFxQUhO0ieOmll+zLL780M7P5%0A8+dbmzZtrKyszDZs2GCZmZk2Y8YMCwQCtnPnTlu2bJmZmXXu3Lk6v6KiIuvcuXN1t0TtC/QuvfRS%0AGz9+vO3bt88qKipszZo11d0P8SgtLbX9+/ebc85WrVpVo9k+3n2cddZZ9l//9V9WWlpqs2bNqtFM%0Av3v3bsvOzrapU6daeXm5zZw50zp27Gi7du06Ip9wn3diaMZv9ACdyEey/+M3F2+uetOYjD1Z9GRj%0AF0WOccn+P1/7avxx48ZZTk6O5eTk2Pjx42tcjf+Xv/zF+vbta5mZmdarVy+bN29eXPt64YUXzDlX%0A4zFmzJjq9UVFRXb++edbhw4drFOnTjZ8+HDbuHFj2PymT59u+fn5lp6ebpdddpnt2bOnxvpJkyZZ%0Ap06drFOnTjZ69Gjbu3evmZkdOnTIMjMzbdWqVSHzve6666xz586WkZFhp5xyis2ePbt63aJFi2zg%0AwIHVV92/+OKLZmb22muvWUFBgWVmZtrw4cPt9ttvrxHsU1JSqoN9SUmJ3Xrrrda9e3dr166dDRgw%0AwF599dW4zqWZVZ/DlJSU6r9V4t3H+vXrbfDgwdamTRv7xje+Uf2ZCD7uU0891TIyMuyb3/ymLV68%0AOGQ+9Qn2up+9xO21la/xg5k/4JcX/ZKfnN0A40FFYuTfx7uxiyFBlixZwpQpU8J2PUjdhfu86372%0A0iCqJtU5GFCfvYjUdPbZZ0ft95ajT1fjS9w0zl5EpGlRsJe4lZWXkeJSFOxFRJoIBXuJW2mglOzW%0A2Qr2IiJNhIK9xK20vJSObTuqz15EpIlQsJe4lZWX0bFNR9XsRUSaCAV7iVtpwKvZK9iLiDQNCvYS%0At9LyUtXsRUSaEAV7iVtVsNfc+CKRFRYWsmDBgsYuRrO2fv16UlJSqKysbOyiJDUFe4lbWXmZmvFF%0AYtAgNzQJY8aMGQwaNIj09HSGDBlS7/ymT59OQUEBGRkZXH755Ufcr/69997jtNNOIyMjg7y8PGbO%0AnFnvfSaLbdu2cckll9CtWzdSUlLYuHFjYxep3hTsJW6lgVI6tOmgYC+SRDp27MjEiRO58847653X%0AihUrqu+2t337dtq2bcttt91WvX7lypWMHDmSRx55hH379vHPf/6T008/vd77TRYpKSkMGzaMWbNm%0ANXZREkbBXuJWWl7KcW2PU7AXicOhQ4e444476NatG926dWPChAkcPny4ev3s2bPp378/7dq1o2fP%0AnsydOzeu/C+88EKuvPJKcnJyQq5funQpgwYNIjs7m/79+/PBBx+Ezevll1/mkksu4ZxzziE9PZ0H%0AHniA119/nYMHva67Bx98kFtuuYWLL76YlJQUsrOzw96Lvrbi4mLOOOMM2rVrR9euXfnxj39cvW7x%0A4sXVZczPz2fq1KkAvP322wwYMIB27dqRn5/PfffdFzb/kpISxo4dS25uLt27d+eee+6Ju4m/c+fO%0A3HLLLZxxxhlxbZfMFOwlblVD7zTOXiR2Dz30EMXFxSxfvpzly5dTXFzMgw8+CHgB8Prrr+fxxx+n%0ApKSEDz/8kMLCQgBuu+02srOzQz769+8f0763bNnC8OHDuffee9mzZw+PPfYYV1xxRch7woNXc+/X%0Ar1/16+OPP55WrVqxevVqAIqKijAz+vbtS25uLqNGjTqimT+c8ePHM2HCBEpKSli3bh1XXXUVABs2%0AbGDYsGGMHz+enTt3smzZsurjy8jIYNq0aZSUlPD222/z1FNPMXv27JD533DDDaSlpbF27Vo+/vhj%0A5s2bx7PPPgt4PybCncvs7Gw++uijmI6hKdKNcCRupYFSslplARCoCNAytWUjl0gkPHdf/fvMbVL9%0A76w3ffp0nnzySY477jgAJk2axM0338z999/Pc889x9ixY7nwwgsByM3Nrd5uypQpTJkypV77njZt%0AGsOGDWPo0KEAXHTRRZxxxhm88847jB49+oj0Bw4coF27djWWZWVlsX//fgA2bdrEtGnTmDdvHjk5%0AOVx//fXcfvvtTJs2LWpZ0tLS+Pzzz9m5cyfHHXccAwcOBLzz8+1vf5urr74agA4dOtChQwcAzj//%0A/OrtTz31VK655ho++OADLr300hp5b9++nXfffZe9e/fSunVr2rRpwx133MEf//hHbrrpJs4555yY%0Af5Q0Nwr2ErfS8lJat2hN25Zt+SrwFe1S20XfSKSRJCJQJ8LWrVspKCiofp2fn8/WrVsB2Lx5M9/9%0A7ncbbN8bNmxg5syZvPnmm9XLysvLueCCC1i8eDH/8R//AXijBz755BMyMjIoKSmpkUdJSQmZmZkA%0AtG3bljFjxtCzZ08A7r77bi666KKYyvLcc89x77330rt3b3r06MGkSZP47ne/y+bNm8N2BRQVFXHn%0AnXeyYsUKDh8+zKFDh6pbBGofZyAQqNGVUVlZSX5+fkxla84U7CVupYFS2rRs83Wwb61gLxJNbm4u%0A69evp3fv3gBs3LiRbt26AZCXl8eaNWtCbld1oVwoVcE5WKir//Pz8xk1ahTPPPNMyHyqauxVTj75%0AZJYvX179eu3atRw+fJgTTzwRgL59+4bMJxY9e/Zk+vTpAMyaNYsrr7ySXbt2kZeXR3Fxcchtrr32%0AWsaNG8fcuXNJS0tjwoQJIbsg8vLyaNWqFbt27SIl5che6kWLFjFs2LCwZZszZ06zvT2v+uwlbmXl%0AZbRp0Yb0lunqtxeJ0YgRI3jwwQfZuXMnO3fu5P777+e6664DYOzYsbzwwgv87W9/o7Kyki1btrBq%0A1SoA/vCHP7B///6Qj+BAX1lZSVlZGYFAgMrKSg4dOkQgEADguuuu480332TevHlUVFRQVlbGwoUL%0A2bJlS8iyjhw5kjfffJPFixdz8OBB7rnnHq644grS09MBGDNmDC+88AJffPEFX331FY8++ijf+973%0AqrcvLCzkxRdfDJn3tGnT2LFjBwDt2rXDOUdqairXXnst7733HjNnzqS8vJxdu3ZV/+A4cOAA2dnZ%0ApKWlUVxczPTp00P+qMnJyeE73/kOEydOZP/+/VRWVrJ27Vo+/PBDAM4999yw53L//v01An1ZWRll%0AZWVHPG+yzKzZPLzDkYaW9UiW7f5qt5065VRbvm15YxdHjmHJ/j9fWFhoCxYsMDOzsrIyGzdunOXk%0A5FhOTo6NHz/eDh06VJ32L3/5i/Xt29cyMzOtV69eNm/evLj29cILL5hzrsZjzJgx1euLiors/PPP%0Atw4dOlinTp1s+PDhtnHjxrD5TZ8+3fLz8y09Pd0uu+wy27NnT431kyZNsk6dOlmnTp1s9OjRtnfv%0AXjMzO3TokGVmZtqqVatC5nvddddZ586dLSMjw0455RSbPXt29bpFixbZwIEDLSsry/Ly8uzFF180%0AM7PXXnvNCgoKLDMz04YPH2633367jRo1yszMvvjiC0tJSbGKigozMyspKbFbb73Vunfvbu3atbMB%0AAwbYq6++Gte5NLPqc5iSklL9t7GF+7z7yyPGR+elax6cc9acjidZpT2Qxr679jH4T4N5YugTnNX9%0ArMYukhyjnHPofz65LFmyhClTpoTtepC6C/d595dHvBJVffYSl4rKCsory2mV2qq6z15EpMrZZ5/d%0AbPu9mzL12UtcysrLaN2iNc450tPSNT++iEgToGAvcakadgeoZi8i0kQo2EtcysrLaNOyDaBgLyLS%0AVCjYS1xKA6W0aeEH+xYK9iIiTYGCvcQluBk/PU3j7EVEmgIFe4lL1ex5oGZ8EZGmQsFe4lI1ex4o%0A2IuINBUK9hKX0nLV7EViVVhYyIIFCxq7GM3a+vXrSUlJifue9ccaBXuJS2kgqM9ec+OLROScCzmH%0Ae0OYMWMGgwYNIj09nSFDhtQ7v+nTp1NQUEBGRgaXX375EbeGfe+99zjttNPIyMggLy+PmTNn1nuf%0AyeLtt9/mnHPOITs7m5ycHG688UYOHDjQ2MWql6jB3jk31Dn3mXPuc+fcz8Kk+Z2/frlzbkC0bZ1z%0AHZxz851zq51z85xz7YPW3eWn/8w5950Q+3rDOfdJ7eVydKgZXyQ5dezYkYkTJ3LnnXfWO68VK1ZU%0A321v+/bhcpVoAAAgAElEQVTttG3blttuu616/cqVKxk5ciSPPPII+/bt45///Cenn356vfebLPbt%0A28e9997Lv//9bz799FO2bNnCT37yk8YuVr1EDPbOuVTgSWAo0AcY4ZzrXSvNMKCnmfUCbgKeimHb%0AO4H5ZnYisMB/jXOuD3C1n34oMMU5lxK0r+8D+wFNht1I1IwvUjeHDh3ijjvuoFu3bnTr1o0JEyZw%0A+PDh6vWzZ8+mf//+tGvXjp49ezJ37ty48r/wwgu58sora9zLPdjSpUsZNGgQ2dnZ9O/fnw8++CBs%0AXi+//DKXXHIJ55xzDunp6TzwwAO8/vrrHDzoteQ9+OCD3HLLLVx88cWkpKSQnZ0d9l70tRUXF3PG%0AGWfQrl07unbtyo9//OPqdYsXL64uY35+PlOnTgW8mvaAAQNo164d+fn53HfffWHzLykpYezYseTm%0A5tK9e3fuueeeuJv4R4wYwXe+8x1at25N+/btufHGG1myZElceSSbaDX7M4E1ZrbezALAK8CltdJc%0AAkwFMLMioL1zrmuUbau38f9e5j+/FPizmQXMbD2wxs8H51wGMAF4EDg67WJyhNJAKa1TNYOeSLwe%0AeughiouLWb58OcuXL6e4uJgHH3wQ8ALg9ddfz+OPP05JSQkffvghhYWFANx2221kZ2eHfPTv3z+m%0AfW/ZsoXhw4dz7733smfPHh577DGuuOKKkPeEB6/m3q9fv+rXxx9/PK1atWL16tUAFBUVYWb07duX%0A3NxcRo0adUQzfzjjx49nwoQJlJSUsG7dOq666ioANmzYwLBhwxg/fjw7d+5k2bJl1ceXkZHBtGnT%0AKCkp4e233+app55i9uzZIfO/4YYbSEtLY+3atXz88cfMmzePZ599FvB+TIQ7l9nZ2Xz00Uch8/zg%0Agw845ZRTYjq+ZBUt2HcDNgW93uwviyVNboRtu5jZdv/5dqCL/zzXTxe8Ta7//AHgMUDRpREF1+w1%0AN740Bc7V/5EI06dP59577+W4447juOOOY9KkSbz00ksAPPfcc4wdO5YLL7wQgNzcXE466SQApkyZ%0Awp49e0I+li1bFtO+p02bxrBhwxg6dCgAF110EWeccQbvvPNOyPQHDhygXbt2NZZlZWWxf/9+ADZt%0A2sS0adN4/fXX+fzzzyktLeX222+PqSxpaWl8/vnn7Ny5k7Zt2zJw4MDq8/Ptb3+bq6++mtTUVDp0%0A6FD9g+P888/n5JNPBuDUU0/lmmuuCdkysX37dt59911+85vf0KZNGzp16sQdd9zBK6+8AsA555wT%0A9lzu2bOHQYMGHZHn/PnzefHFF7n//vtjOr5kFS3Yx9pcHsu/gwuVX9W9eCNt55zrDxxvZrNj3Jc0%0AEPXZS1NjVv9HImzdupWCgoLq1/n5+WzduhWAzZs3c8IJJyRmRyFs2LCBmTNn1qjFLlmyhG3btrF4%0A8WIyMzPJzMzk1FNPBbyadElJSY08SkpKyMzMBKBt27aMGTOGnj17kp6ezt133x32h0Ntzz33HKtX%0Ar6Z3796ceeaZvP3224B3DsJ1BRQVFTFkyBA6d+5M+/btefrpp9m1a1fI4wwEAuTk5FQf5y233MKO%0AHTtiPlfBli5dysiRI5k1axY9e/asUx7JItotbrcAeUGv86hZ8w6VprufpmWI5Vv859udc13NbJtz%0ALgf4MkpeZwFnOOe+8Mvc2Tn3NzO7oHaBJ0+eXP188ODBDB48OMohSjyCr8ZXsBeJXW5uLuvXr6d3%0Ab+/SpY0bN9Ktm9fYmZeXx5o1a0JuV3WhXCiFhYV88knN65VDXf2fn5/PqFGjeOaZZ0LmU1Vjr3Ly%0AySezfPny6tdr167l8OHDnHjiiQD07ds3ZD6x6NmzJ9OnTwdg1qxZXHnllezatYu8vDyKi4tDbnPt%0Atdcybtw45s6dS1paGhMmTAjZBZGXl0erVq3YtWsXKSlH1mUXLVrEsGHDwpZtzpw51bfn/fjjj7n0%0A0kv505/+lJDRDYm0cOFCFi5cGN9GZhb2gRdY1wKFQBqwDOhdK80w4B3/+VnA0mjbAr8EfuY/vxN4%0A1H/ex0+XBvTwt3e19lcAfBKmvCYNa8KcCfarJb8yM7Mt+7ZYzmM5jVwiOZYl+/98YWGhLViwwMzM%0Afv7zn9ugQYNsx44dtmPHDjv77LPtnnvuMTOz4uJia9++vS1YsMAqKips8+bN9tlnn8W1r4qKCist%0ALbWnnnrKzjvvPCsrK7PDhw+bmdmmTZusa9euNnfuXCsvL7fS0lJ7//33bfPmzSHzWrFihWVlZdmi%0ARYvswIEDNmLECBsxYkT1+ueff9569Ohh69ats4MHD9oPfvADGz16dPX6goICmzp1asi8X3rpJfvy%0Ayy/NzGz+/PnWpk0bKysrsw0bNlhmZqbNmDHDAoGA7dy505YtW2ZmZp07d67Or6ioyDp37myjRo0y%0AM7MvvvjCnHNWUVFhZmaXXnqpjR8/3vbt22cVFRW2Zs0a++CDD+I6l5988ol17tzZZsyYEdd2DS3c%0A591fHjmeR00A/wGswrtY7i5/2c3AzUFpnvTXLwdOi7Stv7wD8B6wGpgHtA9ad7ef/jPg4hDlKQT+%0AGaasiTyvEsKtb91qTxY9aWZme0v3WtYjWY1cIjmWJfv/fHCwLysrs3HjxllOTo7l5OTY+PHj7dCh%0AQ9Vp//KXv1jfvn0tMzPTevXqZfPmzYtrXy+88II552o8xowZU72+qKjIzj//fOvQoYN16tTJhg8f%0Abhs3bgyb3/Tp0y0/P9/S09Ptsssusz179tRYP2nSJOvUqZN16tTJRo8ebXv37jUzs0OHDllmZqat%0AWrUqZL7XXXedde7c2TIyMuyUU06x2bNnV69btGiRDRw40LKysiwvL89efPFFMzN77bXXrKCgwDIz%0AM2348OF2++231wj2KSkp1cG+pKTEbr31Vuvevbu1a9fOBgwYYK+++mpc53LMmDGWmppqGRkZ1Y9T%0ATjklrjwaQn2CvbNEdUglAeecNafjSUZjZo/h3Pxz+eGAHxKoCND24bYE7gk0drHkGOWcQ//zyWXJ%0AkiVMmTIlbNeD1F24z7u/POL1bNH67EVqCO6zb5naEoBARaD6uYgc284+++zqfm9JHpouV+ISfDU+%0A6CI9EZGmQMFe4hI8zh40P76ISFOgYC9xCW7GB9XsRUSaAgV7iUtpeama8UVEmhgFe4lLWXlZjWZ8%0ABXsRkeSnq/ElLqWBmjV7zY8vje1o3S9epClTsJe4lJarz16Sh8bYi8RGzfgSFzXji4g0PQr2Epfa%0AzfgK9iIiyU/BXmJmZpSVl9Voxtc4exGR5KdgLzE7VHGIFiktSE1JrV6mmr2ISPJTsJeY1e6vBwV7%0AEZGmQMFeYlZ79jxQsBcRaQoU7CVmtWfPA6/PXsFeRCS5KdhLzMI14+sCPRGR5KZgLzGrPewO1Iwv%0AItIUKNhLzGrPngcK9iIiTYGCvcQsVDN+epr67EVEkp2CvcQsXDO+boQjIpLcFOwlZmrGFxFpmhTs%0AJWalgVJNqiMi0gQp2EvMysrLNM5eRKQJUrCXmIWaVEfj7EVEkp+CvcRM0+WKiDRNCvYSs1BD71qm%0AtgQgUBFojCKJiEgMFOwlZqGa8UH99iIiyU7BXmIWqhkf1G8vIpLsFOwlZqXlRw69A/Xbi4gkOwV7%0AiVmooXegYC8ikuwU7CVmoWbQA82PLyKS7BTsJWahZtADzY8vIpLsFOwlZmrGFxFpmhTsJWa6QE9E%0ApGlSsJeYhRt6p3H2IiLJTcFeYhapGV/j7EVEkpeCvcRMzfgiIk2Tgr3ELNIMegr2IiLJS8FeYqa5%0A8UVEmiYFe4lZqLvegcbZi4gkOwV7iUl5ZTmVVknLlJZHrGvbsi1flatmLyKSrBTsJSZV/fXOuSPW%0Aqc9eRCS5KdhLTMINuwPNjS8ikuwU7CUm4YbdgfrsRUSSnYK9xCTcsDtQM76ISLJTsJeYhBt2Bwr2%0AIiLJTsFeYhJu2B1onL2ISLKLGuydc0Odc5855z53zv0sTJrf+euXO+cGRNvWOdfBOTffObfaOTfP%0AOdc+aN1dfvrPnHPfCVo+xzm3zDm3wjn3nHPuyDFg0mBKA5Fr9pobX0QkeUUM9s65VOBJYCjQBxjh%0AnOtdK80woKeZ9QJuAp6KYds7gflmdiKwwH+Nc64PcLWffigwxX091utKM+tvZicD7fx0cpSUlqvP%0AXkSkqYpWsz8TWGNm680sALwCXForzSXAVAAzKwLaO+e6Rtm2ehv/72X+80uBP5tZwMzWA2uAgX7e%0ABwD8Gn0asDP+w5W6itSMr2AvIpLcogX7bsCmoNeb/WWxpMmNsG0XM9vuP98OdPGf5/rpQu7POTfX%0AT19qZnOilF0SKFIzfsvUljgcgYrAUS6ViIjEokWU9RZjPkdOqxY6zRH5mZk55yLtx4LSXuycawW8%0A6py73sym1k48efLk6ueDBw9m8ODBMRRNoonUjA9f99u3T20fNo2IiNTfwoULWbhwYVzbRAv2W4C8%0AoNd51Kx5h0rT3U/TMsTyLf7z7c65rma2zTmXA3wZIa8tQa8xs0POuVl4zfsRg70kTqQZ9ODrpvz2%0ArRXsRUQaUu2K7H333Rd1m2jN+P8AejnnCp1zaXgXxb1RK80bwGgA59xZwF6/iT7Stm8A1/vPrwf+%0AGrT8GudcmnOuB9ALKHbOpfs/CnDOtQCGAx9HPTpJmNJA+Bn0QP32IiLJLGLN3szKnXM/AuYCqcBz%0AZvapc+5mf/3TZvaOc26Yc24NcBAYE2lbP+tHgRnOubHAeuAqf5uVzrkZwEqgHLjNb+ZPB2b7TfjO%0Az/P5xJ0GiSZaM77mxxcRSV7RmvExs3eBd2ste7rW6x/Fuq2/fDdwUZhtHgYerrXsS7yr+6WRlAZK%0AyUjLCLte8+OLiCQvzaAnMYk09A7UjC8ikswU7CUmkebGBwV7EZFkpmAvMYnaZ6/58UVEkpaCvcQk%0AlmZ8zY8vIpKcFOwlJpFm0AM144uIJDMFe4lJLDPoKdiLiCQnBXuJSbRJddRnLyKSvBTsJSaxTJer%0AcfYiIslJwV5iUlqu6XJFRJoqBXuJSWkghj77cgV7EZFkpGAvMYnWjK+58UVEkpeCvcQklmZ89dmL%0AiCQnBXuJSUzN+KrZi4gkJQV7icrMOFRxSMFeRKSJUrCXqMrKy2iV2ooUF/7jonH2IiLJS8Feooo2%0Aex5obnwRkWSmYC9RRZs9D9SMLyKSzBTsJapow+5AwV5EJJkp2EtU0YbdgYK9iEgyU7CXqKINuwNo%0AmdoSh+NwxeGjVCoREYmVgr1EFUszPqh2LyKSrBTsJapYmvFBwV5EJFkp2EtUsTTjg4K9iEiyUrCX%0AqErLS2Nqxk9PS9f8+CIiSUjBXqIqKy9TM76ISBOmYC9RlQZiq9kr2IuIJCcFe4kqlulyQcFeRCRZ%0AKdhLVLEOvUtvma758UVEkpCCvUQVy9z4oJq9iEiyUrCXqNSMLyLStCnYS1SaQU9EpGlTsJeoYm3G%0AT2+pcfYNYfhw2LatsUshIk2Zgr1EpWb8xvXRR7BuXWOXQkSaMgV7iSrWGfQU7BOvogL27lXNXkTq%0AR8FeooprBr1yBftEKikBMwV7EakfBXuJKtYZ9DQ3fuLt2eP9VbAXkfpQsJeo1GffeHbv9v4q2ItI%0AfSjYS1S6EU7jUbAXkURQsJeodCOcxrN7NxQUKNiLSP0o2EtUsTbjp7dMV7BPsD17oE8fBXsRqR8F%0Ae4kqnrnxdSOcxNq9G3r3hu3bvavyRUTqQsFeotJ0uY1n927o1g3atPn6ynwRkXgp2EtEZuZNqqML%0A9BrF7t2QnQ1du6opX0TqTsFeIgpUBnA4WqS0iJpWwT7x9uyBDh0U7EWkfhTsJaJYh90BtExticNx%0AuOJwA5fq2LF7t4K9iNSfgr1EFOuwuyqq3SeWgr2IJIKCvUQU67C7Kgr2iaU+exFJhJiCvXNuqHPu%0AM+fc5865n4VJ8zt//XLn3IBo2zrnOjjn5jvnVjvn5jnn2getu8tP/5lz7jv+sjbOubedc5865/7l%0AnHuk7octsYqnGR+8+fEV7BPDrGaw3769sUskIk1V1GDvnEsFngSGAn2AEc653rXSDAN6mlkv4Cbg%0AqRi2vROYb2YnAgv81zjn+gBX++mHAlOcc87f5pdm1hsYAJztnBta1wOX2NSlGV83w0mM0lJITfWG%0A3almLyL1EUvN/kxgjZmtN7MA8Apwaa00lwBTAcysCGjvnOsaZdvqbfy/l/nPLwX+bGYBM1sPrAEG%0AmlmpmX3g7yMA/D+gW7wHLPGJddhdFTXjJ05Vfz0o2ItI/cQS7LsBm4Jeb+bIIBsuTW6EbbuYWVXD%0A5Hagi/88108Xdn9+k//38FoEpAGVBtRn31gU7EUkUaIPnoZYJ+l00ZPgQuVnZuaci7Sf6nXOuRbA%0An4Hf+jX/GiZPnlz9fPDgwQwePDiGYkk4sc6eV0Xz4ydOVX89QKdO3uvycmgRy3+tiDRbCxcuZOHC%0AhXFtE8vXxhYgL+h1HjVr3qHSdPfTtAyxfIv/fLtzrquZbXPO5QBfRshrS9DrZ4BVZva7UIUNDvZS%0Af3Vpxtf8+IlRNaEOeH33HTvCjh2Qk9O45RKRxlW7InvfffdF3SaWZvx/AL2cc4XOuTS8i+feqJXm%0ADWA0gHPuLGCv30Qfads3gOv959cDfw1afo1zLs051wPoBRT7eT8IZAETYii3JICa8RtPcDM+qClf%0AROouas3ezMqdcz8C5gKpwHNm9qlz7mZ//dNm9o5zbphzbg1wEBgTaVs/60eBGc65scB64Cp/m5XO%0AuRnASqAcuM1v5u8O3A18Cvw//wL935vZ8wk5ExJSvM34CvaJUzvYd+miYC8idRNT75+ZvQu8W2vZ%0A07Ve/yjWbf3lu4GLwmzzMPBwrWWb0SRAR11peXxD79RnnzjBffagmr2I1J2Cp0RUl2Z8jbNPjOA+%0Ae1CwF5G6U7CXiOKdQU/N+ImjPnsRSRQFe4ko3mZ8BfvEUbAXkURRsJeISgPxDb1LT0vnq3IF+0RQ%0An72IJIqCvURUl7veqc8+MVSzF5FEUbCXiDT0rvHoAj0RSRQFe4lIN8JpHIEAfPUVZGV9vax9eygr%0A85aLiMRDwV4iinfoncbZJ8bevV5wd0F3nHBO97UXkbpRsJeI6tKMr7nx66/2xXlV1JQvInWhYC8R%0AqRm/cdTur6+iYC8idaFgLxGVBjTOvjHUvhK/ioK9iNSFgr1EFO/Qu/Q09dkngoK9iCSSgr1EFO90%0AuW1atOHg4YOYWQOWqvlTn72IJJKCvUQUbzN+y9SWpLgUApWBBixV8xepz15X44tIvBTsJaJ4m/FB%0A/faJoGZ8EUkkBXuJKN5mfFC/fSIo2ItIIinYS1gVlRUEKgK0Sm0V13aaH7/+wvXZd+niBXtdEiEi%0A8VCwl7DKysto1aIVLngatxioGb/+wtXs27aFVq2gpOTol0lEmi4Fewkr3tnzqijY11+4C/Tg69q9%0AiEisFOwlrHhnz6ui+fHrL1zNHtRvLyLxU7CXsOIddldF8+PXj5lXsw/VZw8K9iISPwV7Casuw+5A%0Azfj1tX8/tG4NLVuGXq9gLyLxUrCXsOoy7A4U7OsrUn89KNiLSPwU7CWsujbjq8++fiL114OCvYjE%0AT8FewqpPM77G2dedgr2IJJqCvYSlZvzGEW5CnSoK9iISLwV7Cas+V+Mr2NedavYikmgK9hJWncfZ%0Aa278eol2gV6nTrBrF1RUHL0yiUjTpmAvYZUGSmmdWsc+e42zr7NoNfuWLb1m/h07jl6ZRKRpU7CX%0AsNRn3zii9dmDmvJFJD4K9hJWabn67BtDtJo9KNiLSHwU7CWs0kDdht5pnH39ROuzBwV7EYmPgr2E%0AVZ9mfPXZ151q9iKSaAr2Epaa8RuH+uxFJNEU7CUs3QinccRas9++/eiUR0SaPgV7CauuzfgaZ193%0Ahw5BIADp6ZHTqWYvIvFQsJew6nU/e82NXydVF+c5Fzmdgr2IxEPBXsKq6wx6bVq04avAV5hZA5Sq%0AeYulCR8U7EUkPgr2ElZdh961TG1JikshUBlogFI1b7FcnAdemoMHoays4cskIk2fgr2EVVZeVqdm%0AfFC/fV3FWrN3Drp00UV6IhIbBXsJq67N+KB++7qKZUKdKmrKF5FYKdhLWHVtxgcNv6urWGv2oGAv%0AIrFTsJew6tOMr2BfN7H22YOCvYjETsFewqpPM77mx68b1exFpCEo2EtYdR1nD5ofv67UZy8iDUHB%0AXkIyM8rKy9Rnf5SpZi8iDSFqsHfODXXOfeac+9w597MwaX7nr1/unBsQbVvnXAfn3Hzn3Grn3Dzn%0AXPugdXf56T9zzn0naPlDzrmNzrn9dT9cidXhisO0SGlBakpqnbZXsK8b9dmLSEOIGOydc6nAk8BQ%0AoA8wwjnXu1aaYUBPM+sF3AQ8FcO2dwLzzexEYIH/GudcH+BqP/1QYIpz1ROHzgbOrNfRSszq018P%0A6rOvK9XsRaQhRKvZnwmsMbP1ZhYAXgEurZXmEmAqgJkVAe2dc12jbFu9jf/3Mv/5pcCfzSxgZuuB%0ANcBAP+9iM9NX21FSn2F3oHH2dRVPn32XLl6w16zEIhJNtGDfDdgU9HqzvyyWNLkRtu1iZlVzf20H%0AuvjPc/10kfYnR0F9ht2BmvHrorISSkqgffvoaQEyMqBFC9i3r2HLJSJNX7RgH2udIco9uqrTHJGf%0AeXdLibQf1VsaQX2b8RXs41dS4gXw1Dguk1BTvojEokWU9VuAvKDXedSseYdK091P0zLE8i3+8+3O%0Aua5mts05lwN8GSGvLcRh8uTJ1c8HDx7M4MGD49lcfPUZdgfe3PjbD2ji9njE019fpSrYn3RSw5RJ%0ARJLPwoULWbhwYVzbRAv2/wB6OecKga14F8+NqJXmDeBHwCvOubOAvWa23Tm3K8K2bwDXA7/w//41%0AaPl059yv8ZrvewHF8RxQcLCXuqvPsDvQOPu6qE+wF5FjR+2K7H333Rd1m4jB3szKnXM/AuYCqcBz%0AZvapc+5mf/3TZvaOc26Yc24NcBAYE2lbP+tHgRnOubHAeuAqf5uVzrkZwEqgHLjNb+bHOfdLvB8L%0AbZxzm4A/mtn90U+L1IWa8Y++eC7Oq6JgLyKxiFazx8zeBd6ttezpWq9/FOu2/vLdwEVhtnkYeDjE%0A8p8CP41WXkmM+jbjK9jHTzV7EWkomkFPQiotr9/QO42zj188E+pU6dpV97QXkeiOvWBfXt7YJWgS%0AysrL6t2Mrz77+KhmLyIN5dgK9uXl0K0bbK49oEBqUzP+0ac+exFpKMdWsF+9Gr78EmbNauySJL36%0ANuMr2MevLjX7qln0REQiObaC/fLl0LkzzJjR2CVJevWdQS89TX328apLn33nzrBjB1RUNEyZRKR5%0AOLaC/bJlcPPN8NlnsGlT9PTHsNJA/YfeaW78+NSlZp+WBu3awa5dDVMmEWkejq1gv3w5fPObcNll%0A8NprjV2apFZarj77o60uffagfnsRie7YC/b9+sFVV8GrrzZ2aZJaIu5691XgK0y3ZItZXWr2oGAv%0AItEdO8F++3YoK4O8PLjgAli7Ftavb+xSJa36Dr1rkdKC1JRUApWBBJaq+TKrW589KNiLSHTHTrBf%0Avhz69wfnoGVLuPxyNeVHUN9mfFBTfjxKS72PZps6nHIFexGJ5tgK9v36ff36qqt0VX4E9R16B7pI%0ALx51bcIHBXsRie7YDfaDB3vN+F980VglSmr1bcYH6NimI+v3rk9MgZq5ul6cBwr2IhLdsRvsW7SA%0A738fZs5svDIlsfrOoAdwQ/8bmPKPKQkqUfOmmr2INKRjI9iXlcGaNdCnT83lasoPq763uAUYO2As%0Ac9bMYVOJ5jSIpq4X54GCvYhEd2wE+5UroWdPaF2rD/q887zJddaubZxyJbGy8rJ699m3a92O0X1H%0A82TxkwkqVfOlmr2INKRjI9jXbsKv0qIFXHGFmvJDSEQzPsC4geN47uPnOHD4QAJK1XzVp8++Qwc4%0AcAAOHUpsmUSk+Ti2gz2oKT+MRDTjA/TI7sGQHkN44eMXElCq5qs+NfuUFG+OfN3XXkTCOTaC/bJl%0A4YP9uefC1q3w+edHt0xJrr4z6AWbeNZEnih6gopK3a0lnPr02YPXlL9lS+LKIyLNS/MP9maRa/ap%0AqXDllard11Lfu94F+1bet+ic3pk3Vr2RkPyao/rU7AGGDYMndWmEiITR/IP9pk3ehXlduoRPo6b8%0AIySqGb/KxLMm8uulv05Yfs1NffrsAX76U1i4EJYuTViRRKQZaf7BPlKtvso558DOnd6tb4XyynIq%0AKitomdIyYXle3vtyNpVsonhLccLybE7qW7PPyICHHoIJE7zGLBGRYM0/2Efqr6+SkuI15euqfODr%0A2fOccwnLs0VKC8YPHM9vlv4mYXk2J/XtswcYPRoOH4ZXXklMmUSk+Wj+wb7qBjjRqCm/WqKG3dU2%0A9rSxzFs7T5PshFDfmj14v1mfeAJ+9jP4SvcfEpEgx0awj1azB/jWt7yO05UrG75MSS7R/fVVslpl%0AcUO/G/h98e8TnndTVl4OBw9CVlb98zr3XBg4EH6tyyNEJEjzDvYHDnjD6k48MXralBT4wQ/UlE9i%0Ah93VNm7gOJ7/+Hn2H9rfIPk3RXv3Qvv23kcwEX7xC/jNb7yPvogINPdg/8kn0Lu3N1NeLNSUDyR2%0A2F1tBe0LuPD4C3lhmSbZqZKI/vpgxx8PN94I//3fictTRJq25h3sly2Lrb++ysCBsH8/rFjRcGVq%0AAhqqGb/KxLMm8sRSTbJTJRH99bXdfTfMmQP/93+JzVdEmqbmHexj7a+vUtWU/+qrDVemJqAhm/EB%0ABnYfSE5mDrNXzW6wfTQlDRHss7Lg/vs1FE9EPAr2tVU15R/D35AN2YxfZeJZE/n133UVGdR/Qp1w%0AfvhDKCmBWbMSn7eINC3NN9hXVHh99n37xrfdmWd62z7/fMOUqwlo6GZ8gMu+cRlb92+laHNRg+6n%0AKbnNn+MAABFBSURBVGiImj14M0H/5jfe7HplZYnPX0SajuYb7NeuhU6dvMuc4+EcvPUWTJ4MTz/d%0AIEVLdg01zj5YakqqJtnxJfoCvWAXXOD93v3tbxsmfxFpGppvsK9LE36Vk06C99+Hhx+G3x97Y8LL%0AyssatM++yg8H/JD56+bzry//1eD7SmYNVbOv8qtfeQ/dAlfk2KVgH07PnvDBB1476OOPJ65cTUBp%0AecPX7AEyW2Xyu6G/44KpFzB3zdwG31+yauhg36sXXH893HNPw+1DRJKbgn0khYVewH/6aa+Wf4wo%0ADTR8n32VkX1H8vrVr3PD7Bt4YukT2DF4YWRDXaAX7J57YPZs+PDDht2PiCSn5hvsY7kBTizy8ryA%0A/9JLXj/+MRCMSssbduhdbefkn8PSsUt5YdkL/Ocb/8mh8kNHbd/JoCH77Ku0bw9Tp3ojSx980LsG%0AVUSOHc0z2O/e7Y056tEjMfnl5Hg3C581y5utpJkH/KMx9K62gvYFLPnhEnaX7eaily7iy4NfHtX9%0AN6aGbsavMnSoN8nO++/D+efD+vUNv08RSQ7NM9gvX+5dgpyoycYBunTxviXnzIEf/7hZB/yj2Ywf%0ALCMtg1lXzWJwwWDO/OOZLN+2/KiXoTEcrWAP0L07zJ8Pl18O3/wmvPzy0dmviDSu5hvsE9GEX9tx%0Ax8Hf/gaLF8Ptt0NlZeL3kQSOdjN+sBSXwgMXPMCjFz3KRS9dxF8+/UujlONoMfP67Bu6GT9YSor3%0Ae3XePHjoIRg50rsZj4g0X80z2Ceqvz6U7GyvavSvf3n7mD7du0dpM9IYzfi1XXPKNbw78l3GzRnH%0AQx8+1Gwv3DtwAFq1grS0o7/vAQPgH//w+vP794dFi45+GUTk6GiewX758vhugBOvdu28Jv1f/Qr+%0A8AdvXP4zz8Ch5nFh2dGYQS8WZ+SeQdF/FvHm6jc57ZnTeP7j5ykNlDZ2sRLqaDbhh9K2LfzP/8CT%0AT3ozRf/3f0Mg0HjlEZGG0fyCfSAAq1bBKac07H6c8654+vBD7zLn2bO9e4s+/rhXXWvCjsYMerHK%0Azczlo7Ef8ciFj/D6p6+T/0Q+P53/U77Y80VjFy0hGjvYVxk+3GsQ++c/vRGnd97p/RuJSPPQ/IL9%0AZ59Bfr5XZTlazjkH3n7bexQXe0H/vvu8b/ImqDH77ENJcSkM7TmUt659i6Vjl1JplXzzj9/kkj9f%0Awvy186m0pnvtxNEYYx+rLl3gzTe9vvyKChg8GAYN8hqtSkoau3QiUh/NL9g3ZH99NP37e7fHXbwY%0ANm3yZuEbNQqmTYMvm85QsrLysqRoxg/lhA4n8Nh3HmPjhI1cctIl/Nf8/6LP//Th90W/Z9dXuxq7%0AeHFLlpp9sJNP9nqoNm3yRprOnQsFBd6FfO+912yvSxVp1ppfsG/o/vpYnHgiPPusdxHfOefA6697%0A/fqnnQZ33eX19x8+3LhljCCZmvHDaduyLf952n+y7OZlPHvJsyzZtIQev+1Bvz/04445d/DXz/7K%0AntI9jV3MqI7GhDp11aKF17w/axasWQMDB3p30CsshIkTveXbtjV2KUUkFq45XeXsnDO76CKYMAGG%0ADWvs4tQUCEBRkddGOneu191w3nlw8cVw7rnwjW94l2UngZOnnMwrV7zCqV1ObeyixCVQEeD//v1/%0ALFy/kPfXv8/fN/2dEzqcwJDCIQwuHMx5BefRvnWcd0FsYI8+6jXl/+IXjV2S2C1bBu+8A0uWwN//%0A7v1YOfvsrx99+iR2igsRicw5h5m5iGmaXbDv1Ak+/hi6dWvs4kS2a5fXJjp3rvcjYN06OOEEbzKg%0AU0/9+m9enncx4FF0wu9OYO51c+nZoedR3W+iHa44zD+2/oP3v3ifhRsWsnTzUgraFXBy55Ppc1wf%0A+nTyHr069iIttRHGvuHVlDt2hJ/9rFF2X2+VlfDpp17gX7IEPvoIdu6Eb30LzjzTa9A66SSvsSsj%0Ao7FLK9I8HZvBvmNH2LHjqAfIeisr8741P/nEuyS66lFW5gX+b3zDaz8tKPj6b04OpKYmvCi5j+fy%0Avzf+L92ykvwHU5wOlR/i052fsnLHSlZ8uYKVO1eycsdKNpb8/+2dfWwcxRXAf2/3zvad49gOcRJi%0AO2n+CEhUiAJtoUVt06a0NKJpWhBtJPoBKKpEEUioVWmlVuKvFlQBjSrUSqQqqCofKiriSyVQiASq%0AmpQoUT8MCUFNYkxiO3bsxPdl3+3rHzN3t3c+n53gcPZmftLTvJl5Mze3N7dvdndm9ijrOtaVnP/F%0AF1xMb3sva9rX0N3WTdyPn7M2bdtmnOK2befsIz50BgeN09+718zoP3DAPAZYtqzs/Iuyfr0Zl7cs%0AnPmgDseiY16cvYhcBzwE+MAjqjrthqOIbAe+AqSB76nqvnplRWQZ8CSwFjgM3KSqYzbvJ8CtQAG4%0AU1V32vQrgT8ALcCLqnpXjXaobtxorpijwtCQGQAcOABHjpgNzY8cMTI6avY/XbvWSG+vmVJdlBUr%0ATNjefkaDn877Onn3zndZllhgM8fOEbl8joMjB+kbNs7/4OhB+sf76T/Vz7HTx1ieXF5y/r1Le+ld%0A2kvP0h66WrtY0bqCrmQXyxLL8L0zH3jdcANs3Qo33ngOvtgCIgjg6NGy8w8PAt5/33TR7m7Tnbu7%0AK/XVq6Gry9wBiZ+7cZfDsWj5wM5eRHzgAPBFYAD4J7BVVd8K2WwC7lDVTSJyFfBrVb26XlkRuR84%0Aoar3i8iPgU5VvUdELgH+BHwC6AZeAdarqorIHvs5e0TkRWC7qv61qr2qd999/rx/Pps1Z9Ci8+/v%0AN4ODwcFyODhoNvspOv6uLvOQtSgdHdPiiRc+xchtB0kuW1lzHsGuXbvYsGHDh/99G0A+yHN84jhH%0Ax4+WBgBHx48ycHqA4dQww+lhhlJDjGfH6Ux00pW0A4DWLpYnltOZ6KSjpYOOlg7am9tLelFuun45%0AP/+Zx8aNlf/T8+kYB4G5GTcwAO+9Z8JqfWTEjG1bW82u1bWkvX1maWubPo/gfDrGjcQd53PPXJx9%0AbJY6PgkcUtXDtsIngK8Bb4VsNgOPAqjqbhHpEJFVwLo6ZTcDn7PlHwV2AffY/MdVdQo4LCKHgKtE%0A5AjQpqp7bJnHgC1AhbMHGrfsrhG0tJiHoRddVN8ukzHOvyhjY2ZW2MmT5rKqr68U15Oj5L6eo+Wj%0Al8HpCXNHoK3NPHBta4O2NnYNDbHhssvMmTeZrC8tLWVpbq4db242l2wL8NFLzIvRs7SHnqU90Duz%0AXT7IM5IeYTg9XBoEDKeGGc+NcyJ9gkOjhxjLjjGeG2csO1aS4bdf5stP30rbm++ypGlJSYZfGObS%0AY5eaeHwJyXiSZDxJIp4gEUuU9GQ8WYq3xFpojjWb0G+eFm+ONePJwps553nlm1FXXDGzXRCY9f4n%0ATtSWw4dNfi1JpUwXLkprK4yM7OKSSzaU4sUwmYREor4Uu20ticUWZFduGM7ZLwxmc/bdQH8o/h5w%0A1RxsuoHVdcquVNVBqw8CK62+GvhHjbqmrF5kwKZP53xy9nMlkSjf6p+F7FSGpvs68UZPmre0TE7C%0A6dNlmZiAhx+GLVvMICKdrpQTJ8p6KmXuKmSzlVKdNjlpVivE4+WN4otSjMfjM0s4PxabLtXpvm+k%0AqNdKK4rnVcar82x+zPNY6Xms9H3w2sBrh+aLIeGV7YoiUtLXPNjDqzc/zQUXppjIp5koZJjIZ/jN%0A3h3csH4zE/k0p6dSZApZ0oUMmWyKU4VR0vkMmXyWdD5twwzZfJZcIUcunyvp2Xy2Ih7zYjT5TdOk%0A2W8u6XE/TsyLEffixP14RRjzYhV6tYTTfc/HFx/f803c6tVpnngV6Z54FbbFfE88oyd8Yms8Vq/1%0A6A2lzySCoIFHesInk/ZJpzyyGZ8dv82y5RunSKc9MmmPdEpIpTwyGeHkKSGbsZKFbEbIWD2TgWxW%0AyOWYJtms+R9Vd+OwFLtsdbet1sNpxa5ZS2p125nSanXrWnp1l52LhLp1RTydNndlwmnhsJ7umD9m%0Ac/Zznb03l59FatVnb9HP2yzBlbdkgT2z2jlqoxoQZJ/hq7vB/GTNVpaXbA4c2Mne8Tk+ZPaApJX6%0AHwwaQKDmEq4oGkAhMPmBDXMBZLWcH4TKqpbrUg2lVcfnIITj1Mijyq4Amg/FqWFHRXg8s5pVN17L%0AEiboDMrfc93EBJufejl0HLTyGNQKwxTPlqEzqEoTeV/IxQImYzkjvjAZEyZ9mIwJuZgw5UPegykf%0ApnwTn/KM5EN6wTN2xbS8lUkP0h7kxdgUBAqeVsatnhclCMWNriWbwOqBlPMCgYCQbtOVsl2AVuhq%0A61ObrsDEkQI79/4qVE4JAPVBWxVtpWRbKhc604maf4gJBcGeUAs+mm9hstDEVL6JVBCHQhMUmpFC%0AE+SbkKAJCnETD2JGD5pgMgaZOAQxJIijhTgEcQh8JIih6hv7kvgQxNEgZhoeeDY0ecbet1/Kt2le%0AKO4ZG/VBPTTwQD3zx1XP2palXFZQlcp0PHOAtFinAEJhMsMD28fs3zxkU7RHbH1eSS9vAROYA4wi%0ANizFQzoSjlOOz2ij9m9S1LXkxaptKuqqiFP+vOry1XkV9YbSquI1y1V4V51Bn53ZnP0AlTcve6m8%0Awq5l02Nt4jXSB6w+KCKrVPW4iFwIFLeXm6muAavXqquCoX1Xz/KVHHPh+bfr57/zzr0fTkPOA9qO%0A1U6/t3iZeDaUBiWOemTeKJx12dDpn8oTbx5Y3O/HmG8KhfvPvrA9tNXd2fXuM2M2Z/8msF5EPgK8%0AD3wT2Fpl8yxwB/CEiFwNjKnqoIiM1Cn7LPBd4D4bPhNK/5OIPIC5Tb8e2GOv/k/ZCYB7gG8D26sb%0AO9sEBYfD4XA4zkfqOntVzYvIHcBLmOVzO+xs+u/b/N+p6osisslOpksBt9Qra6v+JfCUiNyGXXpn%0Ay/SJyFNAH2Z4fLuWlwvcjll6l8AsvZs+Oc/hcDgcDsc0IrWpjsPhcDgcjuksvHU4Z4mIXCcib4vI%0AO3btvmOeEZHfi8igiPy70W2JKiLSKyKvich/ReQ/InJno9sUNUSkRUR2i8h+EekTkV80uk1RRUR8%0AEdknIs81ui1RREQOi8i/7DGuOzM9Elf2c9n8x/HBEZHPYGYePaaqi+stOYsEu0fFKlXdLyJLgL3A%0AFteX5xcRSapqWkRiwBvAD1X1jUa3K2qIyN3AlZh9UjY3uj1RQ0T+B1ypqqOz2Ublyr60+Y/dkKe4%0AgY9jHlHV14GF/97YRYyqHlfV/VafwGxCtbqxrYoeqpq2ahNmTtGsJ0vHmSEiPcAm4BHmtjzbcXbM%0A6dhGxdnPtLGPw7FosStZLgd2N7Yl0UNEPBHZj9nU6zVV7Wt0myLIg8CPMNsiOM4NCrwiIm+KSN3X%0AaUXF2S/+ZxEORwh7C//PwF32Ct8xj6hqoKofw+zZ8VkR2dDgJkUKEbkeGLIvRXNX9eeOa1T1csyL%0A6H5gH7XWJCrOfi6b/zgciwIRiQNPA39U1Wdms3ecPao6DrwAfLzRbYkYnwY222fKjwNfEJHHGtym%0AyKGqx2w4DPwF80i7JlFx9qXNf0SkCbOBz7MNbpPDccaIiAA7gD5VfajR7YkiIrJcRDqsngCuBfY1%0AtlXRQlV/qqq9qroO+Bbwqqp+p9HtihIikhSRNqu3Al8CZlwpFQlnr6p5zC5+L2E25HnSzV6ef0Tk%0AceDvwEUi0i8itzS6TRHkGuBm4PN2Oc0+Ebmu0Y2KGBcCr9pn9ruB51T1bw1uU9Rxj1rnn5XA66F+%0A/Lyq7pzJOBJL7xwOh8PhcMxMJK7sHQ6Hw+FwzIxz9g6Hw+FwRBzn7B0Oh8PhiDjO2TscDofDEXGc%0As3c4HA6HI+I4Z+9wOBwOR8Rxzt7hcDgcjojjnL3D4XA4HBHn/w+2hK+sRMYBAAAAAElFTkSuQmCC">
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<p>你会看到，相关系数最终都会收缩到0，尤其当形状参数特别小的时候。</p>

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<h4 id="There's-more...">There's more...<a class="anchor-link" href="directly-applying-bayesian-ridge-regression.html#There's-more...">¶</a>
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<p>就像我前面介绍的，还有一种套索回归的贝叶斯解释。我们把先验概率分布看出是相关系数的函数；它们本身都是随机数。对于套索回归，我们选择一个可以产生0的分布，比如双指数分布（Double Exponential Distribution，也叫Laplace distribution）。</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="k">import</span> <span class="n">laplace</span>
<span class="n">form</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="s2">"loc=</span><span class="si">{}</span><span class="s2">, scale=</span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">g</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">laplace</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">rng</span><span class="p">)),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'r'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Example of Double Exponential Distribution"</span><span class="p">);</span>
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fk4jkTYlYpNzlO+tSXVtvDV26wHvvFT4mEcmbErFIOVuzBj74AHbfvXnPV/W0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%0ArkJggg==">
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<p>留意看x轴为0处的顶点。这将会使套索回归的相关系数为0。通过调整超参数，还有可能创建出相关系数为0的情况，这由问题的具体情况决定。</p>

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